Question

which best explains whether or not all isosceles triangles are similar?
all isosceles triangles are similar. two angles within each triangle are always congruent.
all isosceles triangles are similar. the triangle sum theorem states that the sum of the angles in a triangle is 180°. therefore, the third angle can always be determined.
all isosceles triangles are not similar. the pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
all isosceles triangles are not similar. given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.

Explanation:

Similar triangles require all corresponding angles to be congruent. While all isosceles triangles have two congruent angles, the measure of these congruent angles can vary between different isosceles triangles. For example, one isosceles triangle can have base angles of 70° (vertex angle 40°) and another can have base angles of 50° (vertex angle 80°); their corresponding angles are not congruent, so they are not similar. The correct option clearly states this key reasoning.

Answer:

C. All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.